Mersenne Primes, Polygonal Anomalies and String Theory Classification

It is pointed out that the Mersenne primes $M_p=(2^p-1)$ and associated perfect numbers ${\cal M}_p=2^{p-1}M_p$ play a significant role in string theory; this observation may suggest a classification of consistent string theories.Comment: 10 pages LaTe

Use of forced vital capacity and forced expiratory volume in 1 second quality criteria for determining a valid test

The 2005 American Thoracic Society (ATS)/European Respiratory Society (ERS) spirometry guidelines define valid tests as having three acceptable blows and a repeatable forced vital capacity (FVC) and forced expiratory volume in 1 s (FEV1). The aim of this study was to determine how reviewer and computer-determined ATS/ERS quality could affect population reference values for FVC and FEV1. Spirometry results from 7777 normal subjects aged 8–80 years (NHANES (National Health and Nutrition Examination Survey) III) were assigned quality grades A to F for FVC and FEV1 by a computer and one reviewer (reviewer 1). Results from a subgroup of 1466 Caucasian adults (aged 19–80 years) were reviewed by two additional reviewers. Mean deviations from NHANES III predicted for FVC and FEV1 were examined by quality grade (A to F). Reviewer 1 rejected (D and F grade) 5.2% of the 7777 test sessions and the computer rejected ∼16%, primarily due to end-of-test (EOT) failures. Within the subgroup, the computer rejected 11.5% of the results and the three reviewers rejected 3.7–5.9%. Average FEV1 and FVC were minimally influenced by grades A to C allocated by reviewer 1. Quality assessment of individual blows including EOT assessments should primarily be used as an aid to good quality during testing rather than for subsequently disregarding data. Reconsideration of EOT criteria and its application, and improved grading standards and training in over-reading are required. Present EOT criteria results in the exclusion of too many subjects while having minimal impact on predicted values

Differential geometry construction of anomalies and topological invariants in various dimensions

In the model of extended non-Abelian tensor gauge fields we have found new metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms as well as the exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential gauge anomalies in various dimensions.Comment: 27 pages, references added, matches published versio

Coupled oscillators as models of phantom and scalar field cosmologies

We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.Comment: 18 pages, LaTeX, to appear in Physical Review